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Flare stars across the H-R diagram
Luis Balona
South African Astronomical Observatory
Main results of flare stars observed by Kepler
Flares occur in M, K, G, F and A stars (very few B starsobserved).
Flare stars may be common over the whole spectral range.
Flares tend to occur mostly in rapidly rotating stars.
Flare energies increase with increasing stellar radius.
No support for interacting magnetospheres in RS CVn binarymodel.
The Kepler spacecraft
Continuous photometry of over 100 000 in a broad opticalband (4000–9000 A).
Sampling time of 30 min (long-cadence mode) over 4 years.
Sampling time of 1 min (short-cadence mode) over a fewmonths.
The Kepler input catalogue
Prior to launch, the Kepler field was observed withmulticolour photometry.
For each star, the Teff and radius was derived by a modelingprocess.
Each star can therefore be approximately placed in the H-Rdiagram.
The data
Raw light curves of about 20 000 stars brighter than 12th magwere visually inspected.
Each star classified according to variability type and possibleflares noted.
Eliminated all “flares” which are simultaneous in differentstars.
Omitted all “flares” which did not have the characteristicimpulsive phase.
Avoided noisy stretches in the Kepler data.
Examples of flares: short- and long-cadence
0
5
10
-2 -1 0 1 2 3 4
Time (hr)
10355856
0
5
10
159946017
0
2
4
Par
ts p
er t
ho
usa
nd
6786176
0
5 6545986
0
5
10
15 2557430
0
1
2
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-2 -1 0 1 2 3 4
Time (hr)
9902554
0.5
1.5
2.59778156
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10
20
Par
ts p
er t
ho
usa
nd
7093428
-0.5
1.5
3.5
5.5 6185416
0
0.5
15870686
We use only short-cadence data.
H-R diagram of flare stars - short cadence
-1
0
1
2
4000 6000 8000 10000
log L
/L⊙
Teff
Flares occur even in hottest stars!
Flares in hot stars
Flares in A stars are unexpected.
This indicates that something is wrong with currentunderstanding.
This offers a perhaps important insight into the roles ofconvection and magnetism in generating the corona.
Current view on incidence of flare stars and presence of corona
Stars cooler than granulation boundary (Teff . 7500 K):
Convection → magnetic fields → spots → flares.
Convection/magnetic fields → corona → X-ray emission.
Stars hotter than granulation boundary (Teff & 7500 K):
No convection → no magnetic fields → no spots → no flares.
No convection/magnetic fields → no corona → no X-rayemission.
X-ray detections supports current view
X-ray ”hole” for A stars shows that A stars do not have coronae,as expected.
Flares in A stars
0
2
-2 -1 0 1 2 3 4
Time (hr)
9216367
0
0.58703413
0
0.2
Pa
rts p
er
tho
usa
nd
8351193
0
2
45201872
0
2
4 5113797
0.5
1.5
2.5
-2 -1 0 1 2 3 4
Time (hr)
11189959
0
0.5
1 10489286
0
0.5
1
Par
ts p
er t
ho
usa
nd
8686824
0
20
408142623
0
0.5
13974751
Flares in A stars are not due to a cool companion
-5
-4
-3
-2
-1
4000 5000 6000 7000 8000 9000
log ∆
F/F
Teff
Flare on K companion only
Kepler would be unable to detect a flare on a K/M companion to anon-flaring A star.
Percentage of flare stars as a function of Teff
Type Teff N Nflare Percent
K+M 3000–5000 561 57 10.16
G 5000–6100 2018 99 4.91
F 6100–7600 1617 41 2.54
A 7600–10000 424 10 2.36
0
5
10
4000 6000 8000 10000
Per
cen
tag
e fl
are
star
s
Teff
Selection effects
A flare of a given energy will have a lower amplitude and moredifficult to detect on an A star than on a cool star.
Stellar flares in K/M dwarfs have A- or B-type continuum(Kowalski et al 2013). It is easier to detect such flares on coolstars than on hot stars.
Above selection effects tend to give decrease in flare star numbersfrom M → A, as observed. It is possible that the relative numberof A-type flare stars is not very different from the relative numberof K/M flare stars.
Flares seem to be a general property of all stars and not just cooldwarfs.
Rotational modulation in A stars
0
5
0 1 2 3 4 5
Frequency (d-1
)
4930889 0
1
2
Am
plit
ud
e (
mm
ag
)
4276821 0
3629496 0
0.05 2718321
0
0.01
0 1 2 3 4 5
Frequency (d-1
)
6776957 0
0.01
0.02 6224768 0
0.02
0.04 5371492 0
0.02
5122421
0
0.01
0.02
0 1 2 3 4 5
Frequency (d-1
)
9897254 0
0.01
9839575 0
0.005 8947729 0
5
10 7760680
Most Kepler A-stars show an isolated low-frequency peak.
Very often the harmonic can be detected.
Strongly suggests rotational modulation due to star spots.
Distribution of equatorial rotational velocities
0
0.05
0.1
0.15
0 100 200 300 400
Fra
ctio
n o
f sta
rs
vrot (km s-1
)
Distribution of ve from Kepler photometry (histogram) agrees withdistribution of ve for field A stars (dashed curve).
Revised view on incidence of flare stars
A stars have spots and flares. A stars therefore have magneticfields (but no coronae).
It seems that the presence or absence of X-ray emission (coronae)is independent of the presence of a magnetic field.
On the other hand, X-ray emission stops when convection stops,therefore:
Convection may be necessary condition for the development ofa corona.
Magnetism may play a role in heating, but does not seem tobe primary cause of corona.
What are these flares?
Flares observed by Kepler are white-light flares. White-light solarflares are rare.
Stellar white-light flares may involve processes different fromnormal solar flares.
Flare stars rotate rapidly
0
0.1
0.2
0 10 20 30 40
Period (d)
F stars
0
0.05
0.1Fra
ctio
n
G stars
0
0.05
0.1 K-M stars
Rotation periods from Kepler light curves.
Why is rotation so fundamental in causing flares?
Rapid rotation → young star → activity.
BUT
Perhaps rotation itself plays a role in promoting flares. Perhapsdifferential rotation is efficient at twisting magnetic fields over verylarge distance scales.
Flare energy scales with stellar size
32
33
34
35
36
37
38
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1
log E
log R/R⊙
Fractal nature of magnetic reconnection?
Why do larger stars have more energetic flares?
Energy in magnetic field is given by E = L3B
2
8π
Larger stars → larger L → larger E for a given B .
Observed relation gives B ≈ 30G assuming L ∝ Rstar
Flare shapes
0
200
400
0 0.5 1
Time (hr)
12156549
0
50
100
0 0.5 1
Inte
nsity (
ppt)
8608490
0
50
100
0 0.5 1 1.5 2
4758595
0
5
10
15
-0.5 0 0.5 1 1.5 2
Time (hr)
2557430
0
10
20
30
40
0 0.5 1 1.5
3441906
0
2
4
6
0 0.5 1 1.5
3128488
More than 30% of flares have bumps or change in decay rate.
Interacting magnetosphere model for RS CVn stars
Model for reconnection in magnetic field connecting componentsof RS CVn binary can be tested by looking at flaring rate as afunction of orbital phase.
Flares in eclipsing binaries
0
100
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400
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆K
p (
ppt)
Phase
0
2
4
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8
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12
No. of flare
s
0
100
200
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆K
p (
ppt)
Phase
0
2
4
6
8
No. of flare
s
0
200
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600
0 0.2 0.4 0.6 0.8 1 1.2 1.4
∆K
p (
ppt)
Phase
0
2
4
6
8
10
12
No. of flare
s
No obvious correlation of flaring rate with phase. Interactingmagnetoshere model not supported.
Conclusions
Flares common in M – A stars.
Flares, spots on A stars → convection necessary for a corona.
Rapid rotation promotes flares (differential rotation twisting?).
The larger the star, the more energetic the flare (B ≈ 30G).
Inter-star reconnection not supported for flares in closebinaries.
We need to understand solar white-light flares to understand stellarflares.
